In manufacturing sheet packaging material for containers such as pouches, bags, folding boxes and the like, it is known to remove the longitudinal edge of the sheet to simplify subsequent finishing processes, such as gluing, sealing or folding of the material. In general, the longitudinal edge is thinned out by milling it, and the developing dust is vacuumed off. It is one disadvantage of this milling process that there remains some dust despite the vacuuming which might interfere with the operation of the machine, or it might also adhere to the packaging material itself and thus contaminate it, making the material useless for food packaging purposes. Another disadvantage is that the milling process is of only limited use for such materials as fibers or plastic foil for example. The milling tools become dull very quickly and must be removed and sharpened quite frequently, thus necessitating frequent machine shutdowns and finally causing higher operating costs.